Consider the following statements: 1. The general solution of (d...

Statement 1: The general solution of $\frac{d y}{d x}=f(x)+x$ Now integrating on both side $\int \frac{d y}{d x}=\int[f(x)+x] d x\therefore \quad y=f(x)+C\therefore \quad$ Statement 1 is correct. Statement 2: $\frac{d y}{d x}=f(x)+c$ Squaring both sides, $$\begin{aligned} & \left(\frac{d y}{d x}\right)^2=(f(x)+c)^2 \\ & \left(\frac{d y}{d x}\right)^2=\left[f(x)^2+2 \mathrm{cf}(x)+c^2\right] \end{aligned}$$ Hence, the differential equation is of order -1 and degree -2 . $\therefore \quad$ both Statements 1 and 2 are correct. $\therefore \quad$ Option (C) is correct.